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Introduction

Mathematics Coursework Assignment                 Problem Solving Tasks

My name is…………………; I am currently attending the ……………. Amongst the various subjects I am undertaking this year, is GCSE mathematics. My coursework assignment asks that I seek to stipulate a formula that will help me establish exactly the required amount of spacers necessary for different arrangements of tiles.

I feel the use of diagrams will be useful to depict different arrangements of tiles. Only from these arrangements, will I then be able to collect related information which will then assist me to compile a set of results. Subsequently; I will then organize my results systematically in table form and hopefully from this table I will become aware of a pattern beginning to form. Once I recognize this pattern, I can then determine a suitable formula as a way to work out the required amount of spacers needed for each tile arrangement without having to draw out all diagrams manually. A formula is a rule written in symbols and letters.

Spacers are used when tiling a wall, to make sure the tiles are evenly spaced in straight lines, and that the grout between the tiles is of even thickness. Three types of spacers are used when tiling a wall, these include;

• T spacer
• + spacers &
• Lspacers

My Prediction

‘The L shape spacers required for each tile arrangement will always be 4’

Results Table

I made a table to show my results in

Middle

= (n – 1)2

The ‘term x common difference’ column was removed from the table above due to the fact there is no common difference for this sequence. I have worked out the rule which can be applied to get from one term to the next. This same rule can be applied to find further terms in the sequence.

I am now going to collect another set of results for further investigation. I will start with putting up tiles in a straight line, then look at two rows of tiles, then three rows of tiles and so fourth. As placing the results into table form proved successful, I will repeat the process again. Below I have designed a table, this table shows the arrangement of tiles, the number of each type of spacer used, and the total number of spacers used.

Conclusion table for square tiles (adding one at a time)

Conclusion

Tiling arrangements of different structures could be another investigation of interest. Take for example a T structure or even a cross structure. You could start of with very small diagrams and gradually make them bigger, display some data into a table and look for patterns.

As the American author and philosopher Eric Hoffer says, “The hardest arithmetic to master is that which enables us to count our blessings.” That could be because we’re too busy counting what we don’t have, or what we feel we lack. But now there’s scientific evidence that counting your blessings is actually good for your health!

In one study, some college students were divided into two groups and instructed to keep a diary. One group was told to write about things they were thankful for each day, while the other group was told to write about any problems or simply routine events. Researchers found there were fewer illnesses among the thankful group, and that group also reported exercising more and being more supportive of others. Similar results were also found in other studies.

These experiments demonstrate the mind-body connection. Your thoughts can actually affect your body. When you are focused on the positive, counting the blessings in your life, your body naturally produces the “feel-good” chemical serotonin, resulting in a feeling of calm and well-being. But when you focus on your lack of the negative side of things, you are likewise draining your body of energy and no serotonin is released.

P.S I can see a pattern here, can you?

Claire McIlrath

Claire Mc Ilrath

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

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***
This is a well structured investigation that identifies patterns well. Linear and quadratic sequences are used to generate nth terms that allow the calculation of spacer numbers within any size rectangle and square. Specific strengths and improvements are suggested throughout.

Marked by teacher Cornelia Bruce 18/07/2013

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